In this paper we prove the existence of a weak solution to the following systemDelta_p u = Delta_q v = 0 in Omega|nabla u|^{p-2}partial_{nu}u = f(x,u) - (alpha+1)K(x) |u|^{alpha-1}u |v|^{beta+1} + f_1 on partial Omega |nabla v|^{q-2}partial_{nu}v = g(x,u) - (beta+1)K(x) |v|^{beta-1}v |u|^{alpha+1}+ g_1 on partial Omegawhere Omega is a bounded domain in R^N (N ≥ 2), f_1, g_1, f, g and K are functions that satisfy some conditions.
@article{11313,
title = {Existence for an elliptic system with nonlinear boundary conditions - doi: 10.5269/bspm.v28i2.11313},
journal = {Boletim da Sociedade Paranaense de Matem\'atica},
volume = {28},
year = {2010},
doi = {10.5269/bspm.v28i2.11313},
language = {EN},
url = {http://dml.mathdoc.fr/item/11313}
}
Anane, A.; Chakrone, Omar; Karim, Belhadj; Zerouali, Abdellah. Existence for an elliptic system with nonlinear boundary conditions - doi: 10.5269/bspm.v28i2.11313. Boletim da Sociedade Paranaense de Matemática, Tome 28 (2010) . doi : 10.5269/bspm.v28i2.11313. http://gdmltest.u-ga.fr/item/11313/